Ben Webster
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Moderator ♦
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I'm an Assistant Professor at Northeastern University. My interests are geometric representation theory, knot homology and categorification.
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May 9 |
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Quantized conserved quantities appearing from the Lie-algebra Isn't this essentially the point of Noether's theorem? |
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May 8 |
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What happens to Virasoro at c=25? Andre wants to consider the quotient of the universal enveloping algebra of Virasoro by the relation $k-c\cdot 1$ ($k$ is the central element of the Lie algebra, $c$ a scalar, and $1$ the identity in the UAE). |
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May 2 |
accepted | A question about the proof of Beilinson-Bernstein localisation |
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May 1 |
answered | A question about the proof of Beilinson-Bernstein localisation |
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Apr 24 |
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What are the most important open problems in algebraic combinatorics? I'll just note, this question is not blatantly offensive; I just accidentally clicked the wrong reason to close. I can unilaterally reopen and recluse if people think the reason listed matters (it doesn't). |
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Apr 13 |
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Endomorphisms in Category O and Schubert Classes Mmm, not sure about that; I never really read that book. You should also be able to use the projective $P(w_0w)$ in place of the tilting $T(w)$; for some reason tilting modules felt better when I was writing the answer, but there's a functor that switches projectives and tiltings and induces the isomorphism $P(w_0)=T(e)$ so its essentially the same story. |
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Apr 13 |
accepted | Endomorphisms in Category O and Schubert Classes |
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Apr 13 |
accepted | Springer Action on Centre of Parabolic Category O (after Brundan) |
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Apr 13 |
answered | Springer Action on Centre of Parabolic Category O (after Brundan) |
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Apr 13 |
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Flag Varieties via Quiver Varieties I think the short answer is almost surely not. I don't think I have a truly killer argument that the other $T^*G/B$ is not a quiver variety, but it just feels all wrong. You would need to find a representation of a Lie group where the image of $U(\mathfrak{g})$ in endomorphisms of the representation was canonically isomorphic to $\mathbb{C}[W]$; I have no idea what that would be. |
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Apr 13 |
revised |
Endomorphisms in Category O and Schubert Classes added 298 characters in body |
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Apr 13 |
answered | Endomorphisms in Category O and Schubert Classes |
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Apr 6 |
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Why does the naive choice of homogeneous coordinate ring of a product of projective schemes not work? There's a construction called "multiproj" for rings with several $\mathbb N$ gradings. If you think of $S\otimes S$ as doubly graded and take multiproj, then you'll get the product. You can pass from a multiproj to a project by restricting to a generic ray (if you're lucky), which is what you did. |
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Apr 2 |
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Categorification of WRT invariants of integral homology spheres Last I knew, there were no rigorous mathematical constructions of categorified WRT invariants of 3 manifolds. Of course, lots of people would like to fix this, but at the moment, I don't think anyone knows, say, what replaces S-matrices. |
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Mar 30 |
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Is it true that the geodesics on SO(n) and SU(n) are closed? Reza- This won't work outside $SU(2)$. In a compact Lie group of rank $>1$, you can find irrational geodesics in the torus. |
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Mar 19 |
accepted | Khovanov-Rozansky homology and spectral sequences |
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Mar 19 |
answered | Khovanov-Rozansky homology and spectral sequences |
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Mar 1 |
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D-modules as quantization of modules on cotangent bundle I'm not really sure what question you're asking (perhaps the issue is alluded to in your handle). Geometric representation theorists have certainly noticed that D-modules are quantized coherent sheaves on the cotangent bundle and exploited this fact. So what about it? |
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Mar 1 |
revised |
BGG-like resolutions and translations added 33 characters in body |
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Feb 28 |
answered | BGG-like resolutions and translations |
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Feb 25 |
accepted | A question on Lusztig’s `graph with automorphism' construction? |
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Feb 25 |
answered | A question on Lusztig’s `graph with automorphism' construction? |
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Feb 24 |
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What are some of the math departments in US and Canada that has good research programs in Number Theory Well if you just want a rough sense of which mathematics programs are well regarded USNWR is ok (grad-schools.usnews.rankingsandreviews.com/…). I wouldn't put too much stock in the difference between 30 and 40 on that list, but it will help you catch, for example, schools that are well regarded in general, but with a less prestigious math program. |
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Feb 17 |
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How hard is it to find a tenured position? Yemon- I guess I don't see what contradiction you think is there. Would you think it was strange to say "I'm perfectly happy with my house, but I sometimes wonder if I can find a nicer one"? On the other hand, I don't now what an answer to this question could really look like; the sort of places people at top 20 schools might think of as trading up (Harvard, MIT, IAS) do make tenured hires, though obviously not so many in the grand scheme of things. |
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Feb 17 |
accepted | Covering of Verma modules by translation of a dominant Verma module |
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Feb 16 |
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Covering of Verma modules by translation of a dominant Verma module Jim- Do you think there's something wrong with the direct proof given in my answer? The projective functors used there are translation functors. I also think the OP is just being sloppy about the distinction between translation and projective functors. I think a lot of people say "translation functors" nowadays when they really mean "projective functors." |
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Feb 16 |
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Why are there two Hopf algebra structures on a Kac--Moody Algebra. Sorry about the typo (stupid auto-complete). Anyways, this is too complicated a story to explain in a comment; the elements $k$ behave like they are $q^{H}$ for $H$ in the Lie algebra. There are various answers to what the hell that really means, but you can just calculate without worrying, and everything will be fine. |
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Feb 16 |
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Why are there two Hopf algebra structures on a Kac--Moody Algebra. These are the same Hopf algebra structure, written in terms of different generators. The $k$'s in the quantum group are exponentially of elements of the Lie algebra. |
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Feb 16 |
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Classification of Tori of GL2, up to conjugation Yes, the description is in Aakumadula's comment above. |
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Feb 16 |
revised |
Covering of Verma modules by translation of a dominant Verma module added 487 characters in body |
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Feb 16 |
answered | Covering of Verma modules by translation of a dominant Verma module |
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Feb 3 |
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Analogues of D-modules and constructible sheaves Jan- It is exactly what you are looking for. You are not going to do better than constructible sheaves over a gerbe. |
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Jan 15 |
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Which functions are linear combinations of irreducible characters for a given field $\Bbbk$? You should clarify whether you mean characters of reps over C or over K. |
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Jan 15 |
awarded | ● Favorite Question |
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Jan 13 |
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Lie group action with no slice The action of $\mathbb{R}$ on $\mathbb{R}^2$ by $(x,y)\mapsto (x,y+ax)$ is also a classic. The y-axis is fixed, but has no slice. |
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Jan 8 |
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Dimension of irreducible representations in characteristic p They are "essentially the same" in a much better sense: you choose a basis of the representation so that the group elements are matrices with (algebraic) integer entries; then reducing these modulo p (essentially) produces the irreps over $\bar{\mathbb{F}}_p$. |
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Jan 4 |
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small maps, extension of IC sheaves and BM homology I'm not sure what you mean in item 3 (the VV paper). In what sense does question 1 have an affirmative answer? |
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Jan 4 |
awarded | ● Enlightened |
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Jan 4 |
accepted | Is a fibration in algebraic geometry a fibre bundle? |
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Dec 13 |
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The non-traveling mathematician problem People tend to travel a bit more over the summer, or when on sabbatical, but as fedja points out, then your family can come with you. |
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Dec 13 |
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The non-traveling mathematician problem I agree with fedja that "From talking to other mathematicians, I've realized more and more that traveling to conferences a lot is an important part of being a research mathematician. But I don't want a job where I have to be gone from my wife and children on a regular basis" seems like totally bizarre logic unless you really hate traveling. How often do you think research mathematicians go to conferences? Much of the year we have classes to teach and being gone for more than a week or two a semester is more hassle than it's worth. |
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Dec 3 |
awarded | ● Enlightened |
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Dec 3 |
awarded | ● Nice Answer |
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Nov 26 |
awarded | ● Nice Question |
